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Project: Algorithms for Polycyclic groups associated to number fields and cryptographic applications (DC6) Supervisors: Aurel Page, Bettina Eick Location: Université de Bordeaux, France |
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Hello, I am Alexander Wiesner. I obtained both my Bachelor’s and my Master’s degree in mathematics in my hometown in Germany at the Karlsruhe Institute of Technology. During my studies I mostly focused on algebraic geometry, number theory, and computer science. Now I am pursuing a PhD at the University of Bordeaux under the supervision of Aurel Page, Karim Belabas, Bill Allombert and Bettina Eick, where I analyze polycyclic groups that arise via extensions of submodules in number fields by unit groups. There are three algorithmic problems that I am trying to solve in particular. First, I want to find an efficient way to calculate the group multiplication in these polycyclic groups. Second, I want to solve the isomorphism problem for these types of groups, i.e. I want to know when two groups that I construct are isomorphic to each other, and furthermore, how many different polycyclic groups I can construct when I fix the unit group or the module. The third problem that I am trying to solve is the conjugacy problem in these constructed groups. Based on the results I want to get some cryptographic applications, and if possible, I also want to generalize my algorithms to more general polycyclic groups. |
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